Spring 2010 Algebraic Number Theory
Mathematics G4657 section 001
Last updated on Apr. 1, 2010.
- Course Schedule
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Time: Tuesday 2:30 pm–4:00 pm, Thursday 2:30 pm–3:30 pm
Location: Room 622, Mathematics Building
- Instructor
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Name: Weizhe Zheng
Office: Room 606, Mathematics Building; Phone: 212-854-3003
Email: zheng at math dot columbia dot edu
Office hours: Tuesday and Thursday 10 am–11 am, in instructor's office
- References (incomplete list)
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Algebraic Number Theory, edited by J. W. S. Cassels, A. Fröhlich, Academic Press, 1967.
Algebraic Number Theory, by S. Lang, 2nd ed., Springer-Verlag, 1994.
Algebraic Number Theory, by J. Neukirch, Springer-Verlag, 1999.
- Prerequisites
- Galois theory, commutative algebra
- Lecture Notes
- Abridged notes with no proofs. Updated on Feb. 15, 2010.
- Syllabus
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This syllabus is subject to change.
| Date |
Topic |
| Jan. 26
| global fields
|
| Jan. 28
| places
|
| Feb. 2
| completion
|
| Feb. 4
| extension of places
|
| Feb. 9
|
| Feb. 11
| Dedekind domains
|
| Feb. 16
|
| Feb. 18
| differents and discriminants
|
| Feb. 23
| local fields
|
| Feb. 25
| adeles
|
| Mar. 2
| ideles
|
| Mar. 4
|
| Mar. 9
| Pontryagin duality
|
| Mar. 11
| duality for local fields
|
| Mar. 23
| local zeta functions
|
| Mar. 25
| duality for adeles
|
| Mar. 30
| global zeta functions
|
| Apr. 1
| Kummer theory
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| Apr. 6
| local class field theory: statements
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| Apr. 8
| global class field theory: statements
|
| Apr. 13
| the first inequality
|
| Apr. 15
| Chebotarev's density theorem
|
| Apr. 20
| the second inequality
|
| Apr. 22
| Artin reciprocity
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| Apr. 27
| global existence theorem
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| Apr. 29
| local class field theory
|
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